# Mathematical Modeling and Stability Analysis of a SIRV Epidemic Model with Non-linear Force of Infection and Treatment

## DOI:

https://doi.org/10.26713/cma.v10i4.1172## Keywords:

Vaccination, Local stability, Reproduction number, Steady states, Global stability## Abstract

This paper considers the*Susceptible-Infected-Vaccinated-Recovered*(

*SIRV*) deterministic model with a non linear force of infection and treatment, where individual humans that are vaccinated losses their vaccination after some time and become vulnerable to infections. The basic reproduction number \(R_0\) obtained from the model system is an epidemic threshold that determines if a disease will continue to ravage the human population or not.\ The model state equations considered in this paper possess two steady-state solutions such that if \(R_0<1\), the infection-absent steady-state solutions are locally and globally asymptotically stable. Also, if \(R_0>1\), a unique infection-persistent steady-state solutions are established, which is also locally and globally asymptotically stable. Thus, it leads to the persistence of infections in the human host population. Finally, numerical simulations were carried out to validate our theoretical results.

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*Communications in Mathematics and Applications*,

*10*(4), 717–731. https://doi.org/10.26713/cma.v10i4.1172

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